Variational quantum eigensolver for causal loop Feynman diagrams and directed acyclic graphs

TL;DR

This paper introduces a variational quantum eigensolver (VQE) method to efficiently identify causal, acyclic configurations in multiloop Feynman diagrams, improving detection rates with fewer qubits and circuits.

Contribution

The paper develops a VQE algorithm tailored for selecting acyclic configurations in directed graphs representing Feynman diagrams, offering a quantum approach that outperforms Grover's algorithm in qubit efficiency.

Findings

VQE effectively identifies acyclic configurations in multiloop diagrams.

The method requires fewer qubits and shorter circuits than Grover's algorithm.

Higher detection rates achieved with adapted VQE for degenerated minima.

Abstract

We present a variational quantum eigensolver (VQE) algorithm for the efficient bootstrapping of the causal representation of multiloop Feynman diagrams in the Loop-Tree Duality (LTD) or, equivalently, the selection of acyclic configurations in directed graphs. A loop Hamiltonian based on the adjacency matrix describing a multiloop topology, and whose different energy levels correspond to the number of cycles, is minimized by VQE to identify the causal or acyclic configurations. The algorithm has been adapted to select multiple degenerated minima and thus achieves higher detection rates. A performance comparison with a Grover's based algorithm is discussed in detail. The VQE approach requires, in general, fewer qubits and shorter circuits for its implementation, albeit with lesser success rates.